<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
<!--NewPage-->
<HTML>
<HEAD>
<META http-equiv="Content-Type" content="text/html; charset=UTF-8">
<TITLE>
Erf (Commons Math 3.2 API)
</TITLE>


<LINK REL ="stylesheet" TYPE="text/css" HREF="../../../../../stylesheet.css" TITLE="Style">

<SCRIPT type="text/javascript">
function windowTitle()
{
    if (location.href.indexOf('is-external=true') == -1) {
        parent.document.title="Erf (Commons Math 3.2 API)";
    }
}
</SCRIPT>
<NOSCRIPT>
</NOSCRIPT>

</HEAD>

<BODY BGCOLOR="white" onload="windowTitle();">
<HR>


<!-- ========= START OF TOP NAVBAR ======= -->
<A NAME="navbar_top"><!-- --></A>
<A HREF="#skip-navbar_top" title="Skip navigation links"></A>
<TABLE BORDER="0" WIDTH="100%" CELLPADDING="1" CELLSPACING="0" SUMMARY="">
<TR>
<TD COLSPAN=2 BGCOLOR="#EEEEFF" CLASS="NavBarCell1">
<A NAME="navbar_top_firstrow"><!-- --></A>
<TABLE BORDER="0" CELLPADDING="0" CELLSPACING="3" SUMMARY="">
  <TR ALIGN="center" VALIGN="top">
  <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1">    <A HREF="../../../../../overview-summary.html"><FONT CLASS="NavBarFont1"><B>Overview</B></FONT></A>&nbsp;</TD>
  <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1">    <A HREF="package-summary.html"><FONT CLASS="NavBarFont1"><B>Package</B></FONT></A>&nbsp;</TD>
  <TD BGCOLOR="#FFFFFF" CLASS="NavBarCell1Rev"> &nbsp;<FONT CLASS="NavBarFont1Rev"><B>Class</B></FONT>&nbsp;</TD>
  <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1">    <A HREF="class-use/Erf.html"><FONT CLASS="NavBarFont1"><B>Use</B></FONT></A>&nbsp;</TD>
  <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1">    <A HREF="package-tree.html"><FONT CLASS="NavBarFont1"><B>Tree</B></FONT></A>&nbsp;</TD>
  <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1">    <A HREF="../../../../../deprecated-list.html"><FONT CLASS="NavBarFont1"><B>Deprecated</B></FONT></A>&nbsp;</TD>
  <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1">    <A HREF="../../../../../index-all.html"><FONT CLASS="NavBarFont1"><B>Index</B></FONT></A>&nbsp;</TD>
  <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1">    <A HREF="../../../../../help-doc.html"><FONT CLASS="NavBarFont1"><B>Help</B></FONT></A>&nbsp;</TD>
  </TR>
</TABLE>
</TD>
<TD ALIGN="right" VALIGN="top" ROWSPAN=3><EM>
</EM>
</TD>
</TR>

<TR>
<TD BGCOLOR="white" CLASS="NavBarCell2"><FONT SIZE="-2">
&nbsp;<A HREF="../../../../../org/apache/commons/math3/special/Beta.html" title="class in org.apache.commons.math3.special"><B>PREV CLASS</B></A>&nbsp;
&nbsp;<A HREF="../../../../../org/apache/commons/math3/special/Gamma.html" title="class in org.apache.commons.math3.special"><B>NEXT CLASS</B></A></FONT></TD>
<TD BGCOLOR="white" CLASS="NavBarCell2"><FONT SIZE="-2">
  <A HREF="../../../../../index.html?org/apache/commons/math3/special/Erf.html" target="_top"><B>FRAMES</B></A>  &nbsp;
&nbsp;<A HREF="Erf.html" target="_top"><B>NO FRAMES</B></A>  &nbsp;
&nbsp;<SCRIPT type="text/javascript">
  <!--
  if(window==top) {
    document.writeln('<A HREF="../../../../../allclasses-noframe.html"><B>All Classes</B></A>');
  }
  //-->
</SCRIPT>
<NOSCRIPT>
  <A HREF="../../../../../allclasses-noframe.html"><B>All Classes</B></A>
</NOSCRIPT>


</FONT></TD>
</TR>
<TR>
<TD VALIGN="top" CLASS="NavBarCell3"><FONT SIZE="-2">
  SUMMARY:&nbsp;NESTED&nbsp;|&nbsp;FIELD&nbsp;|&nbsp;CONSTR&nbsp;|&nbsp;<A HREF="#method_summary">METHOD</A></FONT></TD>
<TD VALIGN="top" CLASS="NavBarCell3"><FONT SIZE="-2">
DETAIL:&nbsp;FIELD&nbsp;|&nbsp;CONSTR&nbsp;|&nbsp;<A HREF="#method_detail">METHOD</A></FONT></TD>
</TR>
</TABLE>
<A NAME="skip-navbar_top"></A>
<!-- ========= END OF TOP NAVBAR ========= -->

<HR>
<!-- ======== START OF CLASS DATA ======== -->
<H2>
<FONT SIZE="-1">
org.apache.commons.math3.special</FONT>
<BR>
Class Erf</H2>
<PRE>
<A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">java.lang.Object</A>
  <IMG SRC="../../../../../resources/inherit.gif" ALT="extended by "><B>org.apache.commons.math3.special.Erf</B>
</PRE>
<HR>
<DL>
<DT><PRE>public class <B>Erf</B><DT>extends <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</A></DL>
</PRE>

<P>
This is a utility class that provides computation methods related to the
 error functions.
<P>

<P>
<DL>
<DT><B>Version:</B></DT>
  <DD>$Id: Erf.java 1456905 2013-03-15 11:37:35Z luc $</DD>
</DL>
<HR>

<P>

<!-- ========== METHOD SUMMARY =========== -->

<A NAME="method_summary"><!-- --></A>
<TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
<TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor">
<TH ALIGN="left" COLSPAN="2"><FONT SIZE="+2">
<B>Method Summary</B></FONT></TH>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/special/Erf.html#erf(double)">erf</A></B>(double&nbsp;x)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns the error function.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/special/Erf.html#erf(double, double)">erf</A></B>(double&nbsp;x1,
    double&nbsp;x2)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns the difference between erf(x1) and erf(x2).</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/special/Erf.html#erfc(double)">erfc</A></B>(double&nbsp;x)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns the complementary error function.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/special/Erf.html#erfcInv(double)">erfcInv</A></B>(double&nbsp;x)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns the inverse erfc.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;double</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../../../../org/apache/commons/math3/special/Erf.html#erfInv(double)">erfInv</A></B>(double&nbsp;x)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Returns the inverse erf.</TD>
</TR>
</TABLE>
&nbsp;<A NAME="methods_inherited_from_class_java.lang.Object"><!-- --></A>
<TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
<TR BGCOLOR="#EEEEFF" CLASS="TableSubHeadingColor">
<TH ALIGN="left"><B>Methods inherited from class java.lang.<A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</A></B></TH>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD><CODE><A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#clone()" title="class or interface in java.lang">clone</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#equals(java.lang.Object)" title="class or interface in java.lang">equals</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#finalize()" title="class or interface in java.lang">finalize</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#getClass()" title="class or interface in java.lang">getClass</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#hashCode()" title="class or interface in java.lang">hashCode</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#notify()" title="class or interface in java.lang">notify</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#notifyAll()" title="class or interface in java.lang">notifyAll</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#toString()" title="class or interface in java.lang">toString</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait()" title="class or interface in java.lang">wait</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait(long)" title="class or interface in java.lang">wait</A>, <A HREF="http://download.oracle.com/javase/6/docs/api/java/lang/Object.html?is-external=true#wait(long, int)" title="class or interface in java.lang">wait</A></CODE></TD>
</TR>
</TABLE>
&nbsp;
<P>

<!-- ============ METHOD DETAIL ========== -->

<A NAME="method_detail"><!-- --></A>
<TABLE BORDER="1" WIDTH="100%" CELLPADDING="3" CELLSPACING="0" SUMMARY="">
<TR BGCOLOR="#CCCCFF" CLASS="TableHeadingColor">
<TH ALIGN="left" COLSPAN="1"><FONT SIZE="+2">
<B>Method Detail</B></FONT></TH>
</TR>
</TABLE>

<A NAME="erf(double)"><!-- --></A><H3>
erf</H3>
<PRE>
public static double <B>erf</B>(double&nbsp;x)</PRE>
<DL>
<DD>Returns the error function.

 <p>erf(x) = 2/&radic;&pi; <sub>0</sub>&int;<sup>x</sup> e<sup>-t<sup>2</sup></sup>dt </p>

 <p>This implementation computes erf(x) using the
 <A HREF="../../../../../org/apache/commons/math3/special/Gamma.html#regularizedGammaP(double, double, double, int)"><CODE>regularized gamma function</CODE></A>,
 following <a href="http://mathworld.wolfram.com/Erf.html"> Erf</a>, equation (3)</p>

 <p>The value returned is always between -1 and 1 (inclusive).
 If <code>abs(x) &gt; 40</code>, then <code>erf(x)</code> is indistinguishable from
 either 1 or -1 as a double, so the appropriate extreme value is returned.
 </p>
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>x</CODE> - the value.
<DT><B>Returns:</B><DD>the error function erf(x)
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</A></CODE> - if the algorithm fails to converge.<DT><B>See Also:</B><DD><A HREF="../../../../../org/apache/commons/math3/special/Gamma.html#regularizedGammaP(double, double, double, int)"><CODE>Gamma.regularizedGammaP(double, double, double, int)</CODE></A></DL>
</DD>
</DL>
<HR>

<A NAME="erfc(double)"><!-- --></A><H3>
erfc</H3>
<PRE>
public static double <B>erfc</B>(double&nbsp;x)</PRE>
<DL>
<DD>Returns the complementary error function.

 <p>erfc(x) = 2/&radic;&pi; <sub>x</sub>&int;<sup>&infin;</sup> e<sup>-t<sup>2</sup></sup>dt
 <br/>
    = 1 - <A HREF="../../../../../org/apache/commons/math3/special/Erf.html#erf(double)"><CODE>erf(x)</CODE></A> </p>

 <p>This implementation computes erfc(x) using the
 <A HREF="../../../../../org/apache/commons/math3/special/Gamma.html#regularizedGammaQ(double, double, double, int)"><CODE>regularized gamma function</CODE></A>,
 following <a href="http://mathworld.wolfram.com/Erf.html"> Erf</a>, equation (3).</p>

 <p>The value returned is always between 0 and 2 (inclusive).
 If <code>abs(x) &gt; 40</code>, then <code>erf(x)</code> is indistinguishable from
 either 0 or 2 as a double, so the appropriate extreme value is returned.
 </p>
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>x</CODE> - the value
<DT><B>Returns:</B><DD>the complementary error function erfc(x)
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../../../../org/apache/commons/math3/exception/MaxCountExceededException.html" title="class in org.apache.commons.math3.exception">MaxCountExceededException</A></CODE> - if the algorithm fails to converge.<DT><B>Since:</B></DT>
  <DD>2.2</DD>
<DT><B>See Also:</B><DD><A HREF="../../../../../org/apache/commons/math3/special/Gamma.html#regularizedGammaQ(double, double, double, int)"><CODE>Gamma.regularizedGammaQ(double, double, double, int)</CODE></A></DL>
</DD>
</DL>
<HR>

<A NAME="erf(double, double)"><!-- --></A><H3>
erf</H3>
<PRE>
public static double <B>erf</B>(double&nbsp;x1,
                         double&nbsp;x2)</PRE>
<DL>
<DD>Returns the difference between erf(x1) and erf(x2).

 The implementation uses either erf(double) or erfc(double)
 depending on which provides the most precise result.
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>x1</CODE> - the first value<DD><CODE>x2</CODE> - the second value
<DT><B>Returns:</B><DD>erf(x2) - erf(x1)</DL>
</DD>
</DL>
<HR>

<A NAME="erfInv(double)"><!-- --></A><H3>
erfInv</H3>
<PRE>
public static double <B>erfInv</B>(double&nbsp;x)</PRE>
<DL>
<DD>Returns the inverse erf.
 <p>
 This implementation is described in the paper:
 <a href="http://people.maths.ox.ac.uk/gilesm/files/gems_erfinv.pdf">Approximating
 the erfinv function</a> by Mike Giles, Oxford-Man Institute of Quantitative Finance,
 which was published in GPU Computing Gems, volume 2, 2010.
 The source code is available <a href="http://gpucomputing.net/?q=node/1828">here</a>.
 </p>
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>x</CODE> - the value
<DT><B>Returns:</B><DD>t such that x = erf(t)<DT><B>Since:</B></DT>
  <DD>3.2</DD>
</DL>
</DD>
</DL>
<HR>

<A NAME="erfcInv(double)"><!-- --></A><H3>
erfcInv</H3>
<PRE>
public static double <B>erfcInv</B>(double&nbsp;x)</PRE>
<DL>
<DD>Returns the inverse erfc.
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>x</CODE> - the value
<DT><B>Returns:</B><DD>t such that x = erfc(t)<DT><B>Since:</B></DT>
  <DD>3.2</DD>
</DL>
</DD>
</DL>
<!-- ========= END OF CLASS DATA ========= -->
<HR>


<!-- ======= START OF BOTTOM NAVBAR ====== -->
<A NAME="navbar_bottom"><!-- --></A>
<A HREF="#skip-navbar_bottom" title="Skip navigation links"></A>
<TABLE BORDER="0" WIDTH="100%" CELLPADDING="1" CELLSPACING="0" SUMMARY="">
<TR>
<TD COLSPAN=2 BGCOLOR="#EEEEFF" CLASS="NavBarCell1">
<A NAME="navbar_bottom_firstrow"><!-- --></A>
<TABLE BORDER="0" CELLPADDING="0" CELLSPACING="3" SUMMARY="">
  <TR ALIGN="center" VALIGN="top">
  <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1">    <A HREF="../../../../../overview-summary.html"><FONT CLASS="NavBarFont1"><B>Overview</B></FONT></A>&nbsp;</TD>
  <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1">    <A HREF="package-summary.html"><FONT CLASS="NavBarFont1"><B>Package</B></FONT></A>&nbsp;</TD>
  <TD BGCOLOR="#FFFFFF" CLASS="NavBarCell1Rev"> &nbsp;<FONT CLASS="NavBarFont1Rev"><B>Class</B></FONT>&nbsp;</TD>
  <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1">    <A HREF="class-use/Erf.html"><FONT CLASS="NavBarFont1"><B>Use</B></FONT></A>&nbsp;</TD>
  <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1">    <A HREF="package-tree.html"><FONT CLASS="NavBarFont1"><B>Tree</B></FONT></A>&nbsp;</TD>
  <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1">    <A HREF="../../../../../deprecated-list.html"><FONT CLASS="NavBarFont1"><B>Deprecated</B></FONT></A>&nbsp;</TD>
  <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1">    <A HREF="../../../../../index-all.html"><FONT CLASS="NavBarFont1"><B>Index</B></FONT></A>&nbsp;</TD>
  <TD BGCOLOR="#EEEEFF" CLASS="NavBarCell1">    <A HREF="../../../../../help-doc.html"><FONT CLASS="NavBarFont1"><B>Help</B></FONT></A>&nbsp;</TD>
  </TR>
</TABLE>
</TD>
<TD ALIGN="right" VALIGN="top" ROWSPAN=3><EM>
</EM>
</TD>
</TR>

<TR>
<TD BGCOLOR="white" CLASS="NavBarCell2"><FONT SIZE="-2">
&nbsp;<A HREF="../../../../../org/apache/commons/math3/special/Beta.html" title="class in org.apache.commons.math3.special"><B>PREV CLASS</B></A>&nbsp;
&nbsp;<A HREF="../../../../../org/apache/commons/math3/special/Gamma.html" title="class in org.apache.commons.math3.special"><B>NEXT CLASS</B></A></FONT></TD>
<TD BGCOLOR="white" CLASS="NavBarCell2"><FONT SIZE="-2">
  <A HREF="../../../../../index.html?org/apache/commons/math3/special/Erf.html" target="_top"><B>FRAMES</B></A>  &nbsp;
&nbsp;<A HREF="Erf.html" target="_top"><B>NO FRAMES</B></A>  &nbsp;
&nbsp;<SCRIPT type="text/javascript">
  <!--
  if(window==top) {
    document.writeln('<A HREF="../../../../../allclasses-noframe.html"><B>All Classes</B></A>');
  }
  //-->
</SCRIPT>
<NOSCRIPT>
  <A HREF="../../../../../allclasses-noframe.html"><B>All Classes</B></A>
</NOSCRIPT>


</FONT></TD>
</TR>
<TR>
<TD VALIGN="top" CLASS="NavBarCell3"><FONT SIZE="-2">
  SUMMARY:&nbsp;NESTED&nbsp;|&nbsp;FIELD&nbsp;|&nbsp;CONSTR&nbsp;|&nbsp;<A HREF="#method_summary">METHOD</A></FONT></TD>
<TD VALIGN="top" CLASS="NavBarCell3"><FONT SIZE="-2">
DETAIL:&nbsp;FIELD&nbsp;|&nbsp;CONSTR&nbsp;|&nbsp;<A HREF="#method_detail">METHOD</A></FONT></TD>
</TR>
</TABLE>
<A NAME="skip-navbar_bottom"></A>
<!-- ======== END OF BOTTOM NAVBAR ======= -->

<HR>
Copyright &#169; 2003-2013 <a href="http://www.apache.org/">The Apache Software Foundation</a>. All Rights Reserved.
</BODY>
</HTML>
